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Homework Statement
Two identical coaxial rings ,(radius R each) are kept separated by a small distance d, one of them carrying a charge +Q and the other a charge Q. The charges are uniformly distributed over the respective rings. A point charge q is kept on the common axis of the rings, at a distance R from midpoint of their centers O. The net force on the charge q is (d<<R) (See image of solution)
Homework Equations
Electric field due to dipole on the axis = 2kp/(r^3) (r>>x)
The Attempt at a Solution
I have been taught that if charge and mass density in a body are distributed in same way then I can use position of centre of mass as the position where body acts as if its all charge is concentrated at that position.
Using that result gives me to points where I can assume that system of coaxial rings act as a dipole and electric field due to it and hence force may be calculated at any point.
Seems easy enough to apply in given question where centre of mass is situated at centre of ring.
p= Qd , r=R , E=2kQd/R^3. Clearly incorrect! (Does not tally with given answer!)
So, here is my request 
1. Would someone please explain the answer in image (The part dealing with cos^2 and sin^2)
2. Where is my method incorrect.
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